It really comes down how you describe peaceful. Was there conflict? Yes. On the scale of the wars to come? No. What we see during this time period is the unification of Germany and the start of an arms race within Europe fueled by grudges and nationalism. As powers such as France, Britain and France become more and more paranoid about Germany's growing power they form alliances and build up military to an even more significant level. The time right before WWI may have been peaceful in the sense of lack of big conflict but in reality it was a huge powder keg ready to go off at the drop of a hat just so every country could expand it boarders, exact revenge and show off their military might. Unfortunately a hat did drop with the assassination of Archduke Franz Ferdinand which stated WWI. To sum it up it was peaceful as in the lack of military conflict but if you were to read a newspaper you would see nothing but propaganda getting ready for war.

Edit: Source: my history textbook

There's multiple conflicts in Europe at the time.

Russo-Circassian War 1763–1864.

Circassian tribes openly fight the Russians in the Caucasus.

War of Greek Independence 1821-1832.

Greece, with British, French and Russian support revolts and secures independence from the Ottoman Empire (supported by Egypt).

Belgian Revolution 1830-1831.

Belgium revolts and separates from the Netherlands in a short war.

First Carlist War 1832-1839.

Extended civil war over the throne in France, where multiple European nations, including Russia, Austria and France supports the Carlist pretender.

Sonderbund War 1847.

A brief civil war in Switzerland.

First Schleswig war 1848-1851.

Denmark holds on to Schleswig despite Prussian intervention.

Hungarian Revoluton 1848-1849.

The Austrians, with Russian support, strike down the Hungarians who have declared their own state.

First war of Italian Independence 1848-1849.

The Austrians defeat Sardinia-Piedimonte and the rebels in their northern Italian provinces and retain their territory.

Crimean War 1853-1856.

France, Britain and Sardinia-Piedimonte support the Ottoman Empire against Russian expansionism.

Second war of Italian indepence 1859.

France and Sardinia-Piedimonte defeat the Austrians and Italy can unify.

Second Schleswig war 1864.

Prussia, supported by Austria, defeats Denmark. Holstein and Schleswig are brought to the German Confederation.

Austro-Prussian war 1866.

Prussia defeats Austria over the question of leadership in Germany.

Franco-Prussian war 1870-1871.

Prussia and a coalition of German states defeat France and form the German Empire.

Third Carlist War 1872-1876.

Another civil war in Spain when the Carlist pretender to the throne tries to get it.

Serbo-Ottoman war 1876-1878.

At first an Ottoman victory over Serbia and Montenegro, then, as Russia intervenes, an Ottoman defeat.

Russo-Ottoman war 1877-1878.

Russian and Romanian forces defeat the Ottomans and create Bulgaria.

Graeco-Ottoman war 1897.

Greence declares war against the Ottomans and is defeated.

Italo-Ottoman war 1911-1912.

Italy defeats Ottoman Empire.

First Balkan war 1912-1913.

Greece, Montenegro, Serbia and Bulgaria defeat the Ottoman Empire.

Second Balkan war 1913.

Ottoman Empire, Romania, Greece, Montenegro and Serbia defeat Bulgaria.

These are just the wars in Europe, as you talked about Europe. But there are multiple wars involving European powers in other parts of the world - the Pastry War, the Mexican Empire, the First, Second and Third Opium Wars, the Afghan Wars, the Sindh War, the First Oriental Crisis, the Maori Wars, the Zulu War, the Boer War, the Madhi Rising, the Sepoy Rising and many many more.

I'd say that this era was no less violent than before or after.